Notes on Introductory Combinatorics

• Κύριοι συγγραφείς: Pólya, George (Συγγραφέας), Tarjan, Robert E. (Συγγραφέας), Woods, Donald R. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston : Birkhäuser Boston, 2010.
• Έκδοση: 1st.
• Σειρά: Modern Birkhäuser Classics
• Θέματα: Computer science.; Computers.; Algorithms.; Numerical analysis.; Computer mathematics.; Combinatorics.; Computer Science.; Theory of Computation.; Algorithm Analysis and Problem Complexity.; Computational Mathematics and Numerical Analysis.; Numeric Computing.

 Developed from the authors’ introductory combinatorics course, this book focuses on a branch of mathematics which plays a crucial role in computer science. Combinatorial methods provide many analytical tools used for determining the expected performance of computer algorithms. Elementary subjects such as combinations and permutations, and mathematical tools such as generating functions and Pólya’s Theory of Counting, are covered, as are analyses of specific problems such as Ramsey Theory, matchings, and Hamiltonian and Eulerian paths. This introduction will provide students with a solid foundation in the subject. ---- "This is a delightful little paperback which presents a day-by-day transcription of a course taught jointly by Pólya and Tarjan at Stanford University. Woods, the teaching assistant for the class, did a very good job of merging class notes into an interesting mini-textbook; he also included the exercises, homework, and tests assigned in the class (a very helpful addition for other instructors in the field). The notes are very well illustrated throughout and Woods and the Birkhäuser publishers produced a very pleasant text. One can count on [Pólya and Tarjan] for new insights and a fresh outlook. Both instructors taught by presenting a succession of examples rather than by presenting a body of theory…[The book] is very well suited as supplementary material for any introductory class on combinatorics; as such, it is very highly recommended. Finally, for all of us who like the topic and delight in observing skilled professionals at work, this book is entertaining and, yes, instructive, reading." —Mathematical Reviews (Review of the original hardcover edition) "The mathematical community welcomes this book as a final contribution to honour the teacher G. Pólya." —Zentralblatt MATH (Review of the original hardcover edition). 

 Combinations and Permutations -- Generating Functions -- Principle of Inclusion and Exclusion -- Stirling Numbers -- P#x00F3;lya#x2019;s Theory of Counting -- Outlook -- Midterm Examination -- Ramsey Theory -- Matchings (Stable Marriages) -- Matchings (Maximum Matchings) -- Network Flow -- Hamiltonian and Eulerian Paths -- Planarity and the Four-Color Theorem -- Final Examination.